ERC Advanced Grant · 2022
Automata, Dynamics and Actions
This project lies at the nexus of complex and symbolic dynamics, group theory, decision problems and computation. It aims to solve major problems in each of these fields by means of automatic actions and relations. Finite state automata, pervasive in theoretical computer science, will serve to define self-similar mathematical objects, and produce efficient algorithms to manipulate them. — I will explore a novel notion of automatically acting group, encompassing the previously unrelated notions of automatic groups, automata groups and substitutive shifts. Geometric group theory propounds the vision of groups as geometric objects. A basic notion is volume growth, and Milnor's still open “gap…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.